Front Tracking And Shock Solution For The Global Existence Of One-dimensional Piston Problem

Utilizing front tracking method, this article studies global existence of weak solu-tions including strong shock front of one-dimensional piston problem when the piston velocity is a constant disturbance. Firstly we solve the the Riemann problem, construct approximate solution of one-dimensional piston problem and make a precise estimate of the interaction of the wave and the disturbance wave reflecting on the main shock and the piston. Then we construct Glimm function and prove that the total variation is uniformly bounded. Finally we use the compactness method to prove the global existence of shock solution.